EDEXCEL A-LEVEL PURE MATHS (10): TRIGONOMETRIC IDENTITIES & EQUATIONS

What is a unit circle?

- You can use a unit circle with its centre at the origin to help you understand the trigonometric ratios.

- For a point P(x, y) on a unit circle, such that OP makes an angle Θ with the positive x-axis:

1) cos Θ = x = x-coordinate of P

2) sin Θ = y = y-coordinate of P

3) tan Θ = y/x = gradient of OP

How can you use a unit circle to find the value of sine, cosine and tangent for any angle Θ?

How can you use a unit circle to generate the graphs of y = sin Θ and y = cos Θ?

How can you use a unit circle to find sin and cos values?

How can you use a unit circle to find tan values?

How is the x-y plane divided?

What is an example of deducing the signs of sin Θ, cos Θ or tan Θ in a quadrant?

How can you use the quadrants to determine whether each of the trigonometric ratios is positive or negative?

How can you express acute angles in terms of trigonometric ratios?

What are the exact values of trigonometric ratios?

What is an example of using exact values of trigonometric ratios to find unknown values?

What are the first two trigonometric identities?

What are some examples of simplifying expression with the trigonometric identities?

What is an example of proving identities with trigonometric identities?

What is an example of finding values of trigonometric ratios with trigonometric identities?

What are some simple trigonometric equations?

What are examples of finding solutions to simple trigonometric equations?

What is the principal value?

- The angle you get when you use the inverse trigonometric functions on your calculator.

- The calculator will give principal values in the following ranges:

1) cos⁻¹ in the range 0° ≤ Θ ≤ 180°.

2) sin⁻¹ in the range -90° ≤ Θ ≤ 90°.

3) tan⁻¹ in the range -90° ≤ Θ ≤ 90°.

- The inverse trigonometric functions are also called arccos, arcsin and arctan.

What is an example of solving a simple trigonometric equation in a given interval?

What is an example of finding an error in a given example of solving a simple trigonometric equation in a given interval?

What is an example of finding a value, Θ in a given interval that satisfies a simple trigonometric equation?

What are harder trigonometric equations?

Equations of the form sin nΘ = k, cos nΘ = k and tan nΘ = p.

What are some examples of solving harder trigonometric equations?

What is an example of solving an equation of the form sin (ax + b) = c, cos (ax + b) = c and tam (ax + b) = c?

How can you solve quadratic equations involving sin Θ, cos Θ or tan Θ?

What is an example of solving quadratic equations involving sin Θ, cos Θ or tan Θ?

What is another example of solving quadratic equations involving sin Θ, cos Θ or tan Θ?

EDEXCEL A-LEVEL PURE MATHS CHAPTER TEN: TRIGONOMETRIC IDENTITIES & EQUATIONS

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EDEXCEL A-LEVEL PURE MATHS CHAPTER TEN: TRIGONOMETRIC IDENTITIES & EQUATIONS

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